Introduction

  • The paper focus in regression for count high-dimensional data using GLMs like Poisson or NB.
  • For this reason, LASSO techniques have been proposed for high-dimensional settings in Poisson and negative binomial regression. However, the theoretical ground for high-dimensional count data has been less developed.

Introduction

  • General purpose of the paper.
    • They proposed a penalized maximum likelihood estimator with theoretical guarantees (adaptive minimaxity).
    • Develop computationally feasible methods (convex surrogates) for practical application.
    • Evaluate performance via simulations and real data.

Paper Structure

  • Theoretical Framework. It defines the statistical models (Poisson, NB), proposes the penalized estimation method and provides its statistical properties.
  • Practical Solutions & Analysis: The paper explores LASSO and SLOPE as convex surrogates. It analyzes their theoretical properties, showing SLOPE can retain optimality under specific conditions.
  • Empirical Evaluation: The performance of the practical methods (LASSO, SLOPE) is assessed and compared through simulations and real-world dataset.